even with wifi on, unless you set it to forcibly stay on forever (not possible in the menu I think, but can be done in the config file), it turns off the wifi after a minute anyway. so even with wifi on, technically it's off most of the time.
always-on wifi does eat up the battery rather quickly but unless you mod it, you don't have that
most likely your device is waking up when you don't expect. the magnet sensor should have an half-mode. turn off when cover is closed. require button push to wake up. then the random wakeup problem (every time the cover wiggles a bit) would be gone
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